The first term in a geometric series is $64$ and the common ratio is $0.75$. Find the sum of the first $4$ terms in the series.
Answer: This formula gives the sum ${S_n}$ of the first $ n$ terms in the geometric series where the first term is $ a$ and the common ratio is $C r$ : ${S_n}=\dfrac{ a(1-C r^{ n})}{1-C r}$ We are given the values for $ n$, $ a$, and $C r$. All we need to do is plug them in the formula. We are given that ${n=4}$, ${a=64}$, and $C{r=0.75}$ : ${S_n}=\dfrac{{64}(1-(C {0.75})^{{4}})}{1-C{0.75}}$ Evaluating the expression in the calculator, we get that $S_n=175$. In conclusion, the sum of the first $4$ terms in the series is $175$.